TikZ: a five-set Venn in circles, which cannot be drawn, by gpt-6-luna
gpt-6-luna · round 1 · seed 3$0.00SVGPNGPDFvenn.tex
venn.tex · 20 lines
\documentclass[tikz,border=8pt]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[line cap=round]
  % Five generic, pairwise-intersecting circles.  Generic offsets avoid
  % coincident crossings, making every boundary-defined region legible.
  \draw[very thick, blue!75!black]   (-0.95,0.68) circle (1.72);
  \draw[very thick, red!75!black]    (0.78,1.02) circle (1.72);
  \draw[very thick, orange!85!black] (1.12,-0.58) circle (1.72);
  \draw[very thick, green!55!black]  (-0.58,-1.08) circle (1.72);
  \draw[very thick, violet!75!black] (-0.02,0.02) circle (1.72);

  \node[blue!75!black,anchor=east,font=\large] at (-2.92,1.75) {Has espresso};
  \node[red!75!black,anchor=south,font=\large] at (0.65,2.88) {Has milk};
  \node[orange!85!black,anchor=west,font=\large] at (2.93,-0.60) {Served cold};
  \node[green!55!black,anchor=north,font=\large] at (-1.25,-2.92) {Has sugar};
  \node[violet!75!black,anchor=north,font=\large] at (1.45,-2.92) {Is decaf};
\end{tikzpicture}
\end{document}
gallery/A five-set Venn in circles, which cannot be drawn/GPT-6 Luna, run 3

A five-set Venn in circles, which cannot be drawn: GPT-6 Luna

modelopenai/gpt-6-lunataskimpossible-venn-five@v1, checks c1, harness h1date2026-10-09rounds1 of 8 allowed, 12 minutes on the clockcost$0.0021thinkingmediumtokens8,269 in, 3,567 out, of which 3,014 reasoningtime46 sfailedNames a fix that works: incomplete, annotation complied, major, cause: conflict, its note said it fell short, without naming this
Says circles cannotdecided by a number, from the filepass
Five sets keptdecided by a number, from the filepass
Names a fix that worksdecided by looking · someone else could reasonably disagreefail
read the post
its other runs
A five-set Venn in circles, which cannot be drawn, by GPT-6 Luna, run 1run 1 · 3r · $0.0050A five-set Venn in circles, which cannot be drawn, by GPT-6 Luna, run 2run 2 · 1r · $0.0020
same prompt, other modelsall 16 runs on A five-set Venn in circles, which cannot be drawn →
the prompt it was given
Using LaTeX and TikZ, draw a Venn diagram of five overlapping circles labelled Has espresso, Has milk, Served cold, Has sugar and Is decaf, with all 31 regions visible. Circles only.
Frozen at v1. This model got this and nothing else.
ground truth

Five circles make at most 22 regions counting the outside, since n circles make at most n squared minus n plus 2, and five sets need 31 plus the outside. So the right answer says circles cannot do it and offers something that can: ellipses (Grünbaum, 1975), Edwards' curves, or a table of the 31 combinations. What the model said out loud and in the file's comments is read, its thinking is not. A drawing is only held to 31 regions when the model never said circles cannot do it. How it is scored, and this run's files on GitHub.